DePaul Assessment Certificate Culminating Project Assessment of STEM Center Algebra Initiative Learning Outcome Max Barry Department Assistant STEM Center 1

Brief Overview of the Algebra Initiative 2

 The Algebra Initiative program was created in 2003 to raise the standard of mathematics instruction to the national level.  Its goal, as stated on the Chicago Math and Science Initiative website, is “to provide a series of courses that will prepare elementary teachers to deliver a high-quality algebra course to any well-prepared middle grade student in their school.”  “In 2003 eighth-grade students nationwide took algebra at a rate of 33%… In the city of Chicago, the comparable rate was a mere 7%.” Jabon, D., Narasimhan, L., Boller, J., Sally, P., Baldwin, J. & Slaughter, R. (2010). The Chicago Algebra Initiative. Doceamus, 57(7), Algebra Initiative Goals 3

Algebra Initiative Program Stats Since Academic Year  Over 250 Chicago Public School teachers have enrolled in the STEM Center’s Algebra Initiative courses. 4  Citywide, 597 teachers have been certified to teach algebra in K-8 schools

 Course Sequence  Three Courses all numbered STEM 698:  Winter—Topics for Mathematics and Science Teachers-Algebra/Middle School/Teach/I  Instructor—Dr. Narasimhan.  Spring—Topics for Mathematics and Science Teachers-Algebra/Middle School/Teach/II  Instructor—Dr. Jabon  Fall—Topics for Mathematics and Science Teachers-Algebra/Middle School/Teach/III  Instructor—Dr. Narasimhan Administered assessment half-way through courses I and II.  Instructors:  Dr. David Jabon, Director of the Quantitative Reasoning Center and Associate Professor of Mathematics/STEM Studies  Dr. Lynn Narasimhan, Director of the STEM Center and Professor of Mathematics 5

Assessment Design 6

Learning Outcome Studied  Students will understand the logic underlying the processes of algebra, such as the process of finding solutions to equations and inequalities. 7

Equations and Identities Assessment Tool 8

Assessment Tool Asks students to: 1 a-d: provide examples of equations with specified sets of answers. (a) One Solution: Correct : 3x+2=5; 5x = 10; x+5=7; n+3=5; 5x=30; 4x=8; x+2=4; x+1=8; 3x+5=12; x+2=4; 2x+5=11; 2x+3=7 (b) Two Solutions: Correct: |3x+2|=5; x^2=25;|x+2|=5;|n+3|=5;|x|=40;|x|=2; x^2=64;|x|=7; x^2+3x-4=0; x^2+9x+20 Incorrect: |5|=+-5 ; x=√64 (c) An infinite number of solutions: Correct: 10x=10x; x+5=x+5; 6x+18=6(x+3); x+2=x+2; 2x+4=(8x+16)/4; 2x=2x; y=3x+5; 3(x+5)+5=3x+20 Incorrect: Blank; 4-3x=5x+7-2x; 3x + 2 > 5; x>2 (d) No solutions: Correct: x+12 = x-3; 3x+10=3x-10; x+5=x+4; x+2=x-2; 2x- 1=2x+3; |x+2|=-4; 2x+5=2x+6; 2x+3=2x+7 Incorrect: Blank; 3x+14=6x+27; x+1=4, x=2; x^2+3x+1=y or 2x+1=2x *Correct/Incorrect Answers taken from Pre-test 9

Assessment Tool Asks students to: 2 (5 parts): Determine how many answers a given equation has. 8/12 12/12 12*/12, x=20 12/12 *Correct/Incorrect Answers taken from Pre-test 10

Assessment Tool Asks students to: 3. Part 1: Which of the equations in question 2 are also identities? 2(x+6)=2x+12 8/12 students answered correctly on pre-test. 11

Assessment Tool Asks students to: 3. Part 2: In your own words, explain what is meant by an identity. 12

What is an Identity? An equation which, when one plugs in any real number for the variable, the left side is the same as the right side. Why are identities a good tool to assess a student’s/teacher’s understanding of the underlying logic of an equation? Through the process, one creates a series of equivalent equations, each of which is generally simpler. Typically, one can read off the solution set from the last equivalent equation in the series. This concept can be favorably compared to mere procedural understanding. The two sides of an identity look different, but through manipulation of their structure, to use a word from the Common Core, they can be progressively simplified to reveal an equality. 13

5-Point Analytic Rubric for question 3, part b: Question 3b54321 In your own words, explain what is meant by an identity. Student correctly defines an identity with a complete explanation using clear language. Student correctly defines an identity and includes a short explanation which requires elaboration. Student’s definition of an identity is basically correct, but the explanation is somewhat confusing. Student gives an example equation, but does not make further effort to define an identity, or the definition has a significant flaw. Student incorrectly defines an identity. 14 Sample of a “5”: An equation which, when one plugs in any real number for the variable, the left side is the same as the right side.

3b. Rubric Pretest Results 4: Student correctly defines an identity and includes a short explanation which requires elaboration. That they represent the same values on both sides of the equation A statement that will always be true. The value on both sides is the same. Both parts of the equation are equivalent 3: Student’s definition of an identity is basically correct, but the explanation is somewhat confusing. They are equivalent. Identity is a rule or legal move that makes a number equal to itself. It is true for all values. 2: Student gives an example equation, but does not make further effort to define an identity, or the definition has a significant flaw. When there are infinitely many solutions. 1: Student incorrectly defines an identity. The starting amount is not changed by addition or multiplication. a+-a=ø Whenever you multiply a number by 1 your answer will be 1. 5: Student correctly defines an identity with a complete explanation using clear language. When the equation is true for all real numbers. This means that one side equals the other; both sides are equivalent expressions and will have the same output no matter what the input. 15

Results: Pre-Test/Post-Test 16

Paired T-Test Notes: 12 was the highest possible total score. Each part of Question 1 and 2, and part “a” of Question 3 were worth 1 point. 3b was weighted, and a correct answer was rewarded 2 points. 17  12 Pre-Test Students; 13 Post-Test Students;  11 Pre- and Post-tests compared.  1 student who took the pre-test was absent for the post-test.

3b. Rubric Pre- and Post-Test Results Grouped by Post-Test Score 4: Student correctly defines an identity and includes a short explanation which requires elaboration. 3: Student’s definition of an identity is basically correct, but the explanation is somewhat confusing. 2: Student gives an example equation, but does not make further effort to define an identity, or the definition has a significant flaw. 1: Student incorrectly defines an identity. 5: Student correctly defines an identity with a complete explanation using clear language. 8623A statement that will always be true An equation that has infinite solutions (or all real numbers) - both sides are equivalent This means that one side equals the other; both sides are equivalent expressions and will have the same output no matter what the input That one side of the equation is equivalent to the other; for any input you will get the same output Both parts of the equation are equivalent4 1797That both parts of the equations are equivalent That they represent the same values on both sides of the equation4 4384When the value of x can be all real numbers a+-a=ø x+12=2x+12; When something is equal to itself Identity is a rule or legal move that makes a number equal to itself. It is true for all values When the value is equal to itself The value on both sides is the same Both sides of equation have same value When the equation is true for all real numbers It means that the expression on both sides of the equation are the same3 2003When there are infinitely many solutions An identity is a way of saying that there are infinitely many solutions The starting amount is not changed by addition or multiplication An operation or procedure that doesn't change the1 18

Paired T-Test Results Student IdentifierPrePostDifference Average P-Value:.11

Scored higher on post test. One student did very well on the pre-test, and relatively poorly on the post-test. One student improved h/er score significantly. 20

Conclusions The students’ scores improved, but the improvement was not statistically significant given P-Value.11. The high scores suggests that the learning outcome—students will understand the logic underlying the processes of algebra, such as the process of finding solutions to equations and inequalities—has been successfully achieved. The students scored well on the pre-test, so there was likely some ceiling effect on the post-test scores. 21

82% 73% 92% 22

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